Question
Asked Oct 21, 2019

This problem is (11.3) from a book  "Thermodynamics and Statistical Mechanics An Integrated Approach by M. Scott Shell"

11.3. Show that cy and cp are
always positive
as T is positive.
long
as
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11.3. Show that cy and cp are always positive as T is positive. long as

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Step 1

By helping  to the first law of thermodynamic equation 1 is converted in terms of CV and ideal gas law.

After converting equation 1 result equation 2 because enthalpy is the function of f (T, V).

du Pdv
Tds
CudT
dv
CT,v)
ds
)av
T
CA
CA
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du Pdv Tds CudT dv CT,v) ds )av T CA CA

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Step 2

Equation 2 multiply by T and get equation 3, in terms of enthalpy at constant volume converted into CV/T sub-equation (a) and first Maxwell relation sub-equation (b). Put in the equation 3.

Found that first TdS relation equation 4.

Tds=
TS
dT T
T
Ca)
Fisst mawl
Pslatioon
LSP
vT
dP
CydT T
dv
Tds
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Tds= TS dT T T Ca) Fisst mawl Pslatioon LSP vT dP CydT T dv Tds

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Step 3

Behalf of third Maxwell relation got that equation 5, arranging the equation in terms of temperature equation 6 write that. ...

Tds
dPA-4p
R dP
P
dP
CpdT
T
[T, F]
z
ds
dT
= S
T
T dsT
T S
d T
T
T T
CA
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Tds dPA-4p R dP P dP CpdT T [T, F] z ds dT = S T T dsT T S d T T T T CA

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